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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.10759 |
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| _version_ | 1866929229428424704 |
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| author | Suragan, Durvudkhan Talwar, Bharat |
| author_facet | Suragan, Durvudkhan Talwar, Bharat |
| contents | We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension $Q$. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon a group element and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10759 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fujita exponent on stratified Lie groups Suragan, Durvudkhan Talwar, Bharat Analysis of PDEs 35R03, 35B33, 35B44 We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension $Q$. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon a group element and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem. |
| title | Fujita exponent on stratified Lie groups |
| topic | Analysis of PDEs 35R03, 35B33, 35B44 |
| url | https://arxiv.org/abs/2211.10759 |